I'd call that 'running two psu's parallel'. You can run two concurrently with a relay, no problemo.
Give it a whirl. You might melt a psu, melt a mainboard lead, knock out a processor/vid. card on a permanent basis, or even a hard drive.
At the very least, I'd go with two supplies that have the exact same wattage, physically look identical (except for the placement of the 'pot ok' stickers) which includes manufacturer, and run off the same power cord (i.e. spliced into). Even a .1v difference can cause some interesting current flows through those transformers.
Rich is the nation that has many war heroes. Long since forgotten...